Chris Kirkland, Glenn Loovens, Jose Semedo, Kieran Lee and Chris Maguire have all had new deals put to them by the Owls, but none have put pen to paper as yet.
Palmer is hoping that their futures are secured soon, though, as he feels that they can all offer a lot to Wednesday next season.
“Those five are big players for us so it’s great to see them offered contracts," he said.
“The sooner they sign the better so we can keep that core together and then it’s definitely a case of bringing in a few more. Hopefully those deals can get sorted and them five will stay."
If Wednesday are able to retain the services of the five out of contract players, the competition for places in the Owls' squad will be fierce.
Palmer can still feel relatively assured of his position, though, as he has always been reliable when called upon.
Wednesday are expected to bring in a number of new signings over the summer, as they now have funds available to manager Stuart Gray following the takeover of Dejphon Chansiri.
The Yorkshire outfit will be among the favourites to secure promotion out of the Championship next term and, as a result, a lot of changes are expected at Hillsborough in the coming weeks.